1. Some people just learn them by the initial letters SOHCAHTOA (soh-cah-toa)
So,
Sine is Opposite over Hypotenuse, Cos is Adjacent over Hypotenuse and Tan is Opposite over Adjacent.

2. You could try a mnemonic (a phrase made up by using the first letter of each word.
Here's one we've made up:

Sweaty Old Horses Chase After Hens That Offer Advice.

OK, that was shocking. You can probably make up a much better one of your own! Once you think you have got it in your head, try the test below.

Drag the labels on the triangle into the formula and mark your answer:

3. Formula Triangles - these have the added advantage of giving you the different arrangements of the formulas you need! You may have used them before in Physics. All you do is cover what you want to calculate and what's left is the formula to calculate it. The diagram below shows how this works.

Here's a worked example showing how to find a side. Again, we've called the side we want to find x.